Determine the measure of the unknown angle in the triangle.

65°

Step-by-step explanation:

Let the unknown angle be ∠ABC

∠ABC + 78° + 37° = 180° (angle sum property of a triangle)

∠ABC + 115° = 180°

∠ABC = 180° - 115°

∠ABC = 65°

∴the unknown angle in the triangle is 65°

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4